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Vector databases are increasingly deployed as retrieval pipelines in which representation, indexing, and query-time execution jointly determine accuracy, throughput, and cost. Existing vector database evaluations primarily focus on indexing while treating embeddings as fixed inputs and ignoring the role of query-time execution, making it difficult to decide whether a bottleneck should be addressed by changing the embedding model, the index, or the query-processing stages. To address the above limitation, we introduce \textbf{VecDBLens}, a modular attribution framework that treats the component under diagnosis as an \emph{evaluated object} and all remaining dataset, workload, parameter, and runtime factors as matched \emph{evaluation conditions}. VecDBLens reports stratified marginal effects, paired matched-condition differences, Flat-relative retention, and monotonicity audits, thereby turning vector database benchmarking from leaderboard ranking into a reproducible diagnostic procedure. VecDBLens reveals two key insights. First, retrieval performance is fundamentally upper-bounded by embedding quality, revealing that many apparent indexing failures are therefore representation-side limitations. Second, stronger index parameterization is not always beneficial: overly aggressive configurations can reshape neighborhood topology and cause recall regression. These results challenge the common practice of evaluating vector databases primarily through indexing and show that real-world limitations emerge from stage-wise constraints rather than any single module alone. VecDBLens provides a principled basis for identifying the true performance drivers of vector databases and for guiding their design in practical applications. The code is available at \url{https://anonymous.4open.science/r/VecDBLens-83A4}.

We investigate a general-purpose layer for deep learning that, instead of compressing arbitrary-size training data into fixed-size weight matrices, stores a new pair of key-value representations for every data point during training, and retrieves and recombines these representations through an attention mechanism at inference time---resulting in a growing neural net (NN). We derive such a "retrieval-centric deep learning" (RCDL) paradigm from the classic duality of a linear layer trained by gradient descent as a type of linear attention (LA) over the training data points---which motivates us to replace the corresponding LA by a more powerful form of attention from recent work on sequence models, namely, kernelized attention using radial basis function (RBF) and softmax-like kernels, as well as more advanced linear attention variants such as MesaNet and DeltaNet. We theoretically derive learning algorithms for the growing layers with kernelized attention, and empirically demonstrate their promising performance and sample-efficiency on classic image classification tasks and synthetic teacher-student learning datasets. In the MesaNet/DeltaNet-inspired extensions, we show a formal connection to a recently proposed optimizer and derive highly sample-efficient optimizers for conventional fixed-size NNs. Despite open challenges, RCDL represents a promising paradigm for nonparametric machine learning.

Multilingual Information Retrieval reflects real-world search settings where users issue queries over mixed-language corpora. Existing evaluations mainly reward language-agnostic semantic relevance, treating relevant passages equally regardless of language. Yet retrieval utility also depends on the language of the retrieved passages: users expect results they can read and verify in the query language, and query--passage language mismatch can complicate downstream grounding in Retrieval-Augmented Generation systems. To evaluate this aspect, we introduce **MLAIRE**, a **M**ultilingual **L**anguage-**A**ware **I**nformation **R**etrieval **E**valuation protocol that disentangles cross-lingual semantic retrieval from query-language preference. MLAIRE constructs controlled pools with parallel passages across languages, enabling measurement of whether retrievers find relevant passages and whether they prioritize query-language passages when equivalent translations are available. We further propose language-aware metrics, including Language Preference Rate (LPR) and Lang-nDCG, together with a 4-way decomposition separating semantic and language-preference failures. Evaluating 31 dense, sparse, and late-interaction retrievers, we show that standard metrics obscure distinct behaviors: semantically strong retrievers may return correct content in a non-query language, while language-preserving retrievers may retrieve less relevant passages.

In long-context use, large language models frequently synthesize answers from the meaning of a relevant context span rather than literally copy-pasting them. Identifying which attention heads perform this synthesis matters for interpreting long-context model behavior. Yet existing detectors miss these heads by construction: they reward heads whose attended token matches the generated token, a literal-copy criterion that captures where a head reads but not what it writes through its output-value (OV) circuit, the very mechanism that carries non-literal retrieval. We introduce Logit-Contribution Scoring (LOCOS), a write-aware detector that scores each head by the projection of its OV-circuit output onto the answer-token unembedding direction, contrasting needle and off-needle source positions in a single forward pass. Across three model families (Qwen3, Gemma-3, OLMo-3.1), mean-ablating the top LOCOS heads on the NoLiMa non-literal retrieval benchmark collapses ROUGE-L at lower head counts than every attention-based baseline; on Qwen3-8B, ablating 50 heads drives ROUGE-L from 0.401 to 0.000 while the strongest baseline still retains 0.292. The selected heads are retrieval-specific: parametric recall and arithmetic reasoning stay at baseline under the same ablation.

Why does the low dimensionality of representations, typically $d\approx 1000$, not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of data points? To answer this question, we study maximal-margin embeddings in the following retrieval model, classically studied in communication complexity [PS86] and more recently in embedding-based retrieval [WBNL25]. Let $A$ be a binary $N\times n$ matrix indicating whether each of $N$ queries is relevant to each of $n$ documents. We are interested in the largest margin $m>0,$ denoted by $\mathsf{m}^{\mathsf{rd}}(d, A),$ for which there exist unit norm embeddings of the queries and documents $U_1, U_2, \ldots, U_N, V_1, V_2, \ldots, V_n$ with the following property. $\langle U_j, V_i\rangle \ge m$ whenever $A_{ji} = 1$ and $\langle U_j, V_i\rangle \le -m$ when $A_{ji} = 0.$ A large margin is a key proxy for representation quality: it controls both robustness to perturbations and compositional generalization across queries. Our main theorem establishes that the best possible margin without a restriction on the dimension, $\mathsf{m}^{\mathsf{rd}}(+\infty, A),$ can be nearly achieved in dimension $d = O(\mathsf{m}^{\mathsf{rd}}(+\infty, A)^{-2}\log n)$ which improves a theorem of [BDES02]. Together with a matching lower bound in Theorem 1.5, we conclude that when $A$ is the $\binom{n}{k}\times n$ matrix containing all possible $k$-sparse rows once, dimension $d = O(k\log (n/k))$ is necessary and sufficient for the maximal possible margin $\mathsf{m}^{\mathsf{rd}}(+\infty, A) = \Theta(k^{-1/2})$ in this setting. This fully resolves the setup of [WBNL25]. We also give several constructions for large margins when $d = o(k\log (n/k)).$ Our proofs are based on connections between this problem and the literature on compressed sensing and the restricted isometry property. Finally, we empirically test the InfoNCE and sigmoid losses for producing large margin embeddings and demonstrate a clear advantage of the sigmoid loss.

When a text description is extended with an additional detail, image-text similarity should drop if that detail is wrong. We show that CLIP-style dual encoders often violate this intuition: appending a plausible but incorrect object or relation to an otherwise correct description can increase the similarity score. We call such cases \emph{half-truths}. On the verified COCO evaluation set, CLIP prefers the correct shorter description only 41.0\% of the time, and performance drops to 28.2\% when the added detail is a relation. We trace this vulnerability to weak supervision on caption parts: contrastive training aligns full sentences but does not explicitly enforce that individual entities and relations are grounded. We propose CS-CLIP (Component-Supervised CLIP), which decomposes captions into entity and relation units, constructs a minimally edited foil for each unit, and fine-tunes the model to score the correct unit above its foil while preserving standard dual-encoder inference. CS-CLIP raises half-truth accuracy to 78.2\% and improves average performance on established compositional benchmarks by 5.7 points, suggesting that reducing half-truth errors aligns with broader gains in compositional understanding.

Multimodal generative retrieval formulates multimodal retrieval as discrete identifier generation, eliminating the need for explicit similarity search over external embeddings. Existing approaches construct identifiers via residual quantization and decode them with trie-constrained beam search. This combination introduces an indexing–decoding gap: identifier learning objectives, including reconstruction and contrastive losses, do not explicitly enforce prefix discriminability during decoding. As a result, even well-optimized identifiers can be irreversibly pruned early in beam search due to low-rank prefixes. We theoretically characterize this gap and derive a survival bound that relates prefix retention to three controllable factors in indexing and decoding. Building on this bound, we propose PRO, prefix retention optimization, a unified framework comprising three mechanisms: (i) prefix ranking distillation aligns quantized prefix rankings with those induced by pre-quantization embeddings using a listwise loss; (ii) vocabulary scheduling increases codebook sizes from shallow to deep residual quantization levels to reduce early competition from non-target prefixes; and (iii) geometric score fusion vectorizes each candidate prefix and incorporates its similarity to the query into beam search scoring, further reducing the indexing–decoding mismatch. Experiments on nine multimodal retrieval tasks show that PRO improves retention of target identifier prefixes and outperforms existing multimodal generative retrieval baselines.